Elasticity is an important property of both animate and inanimate objects, covering their rigidity (flexibility) and structure survival. In both types of objects, this property is far from being completely understood, in fundamental ways. For animal structures, this concern is particularly vital and especially critical in maintaining the essence of life. Elasticity is intricately involved, in pathological diseases, and in the intrusion through and fluidity of cellular membranes, on the microscopic level. Also, some features, in the mechanism of aging, is implied in the analysis. Elasticity physics, of microemulsions (complex fluids of swollen micelles originating from the admixture of water and a surfactant in oil environment), -vesicles, and -cellular membranes, is essentially the same. Therefore, elastic information, about one of these structures, has implications for the others. Because of their simplicity and electro-optical behavior, as shown by us and others, microemulsions will be used as test materials to measure elasticity of vesicles and cell membranes. Specifically, we will: (1) use the Electro-Optical Birefringent (EOB) Kerr coefficient method to measure, in different aliphatic oil environments and at different temperatures, the Kerr co-efficient dependence on swollen- micellar droplet size omega (molar ratio of the number of water molecules to the number of surfactant molecules); (2) modify using the Mean Field Theory, Numerical Analysis, and the Calculus of Variations the single isolated droplet model; and (3) reconsider the data obtained in #1, above, based on the modified theory for the advantages of one model over the other. These research efforts will impact directly on the health of mankind by providing information on pathological diseases and the essential deterioration of cell membrane-liked structures. Our measurements and modeling developments are essential for subsequent-direct characterization of cellular membranes.